Wragg became a school governor in 2008 and went on to volunteer as a student mentor.[4] He unsuccessfully stood as the Conservative candidate in the Hazel Grove ward of Stockport Metropolitan Borough Council in 2010,[5] but was subsequently elected in the same ward a year later in 2011.[6] He completed the Teach First programme, a scheme to encourage top graduates into the teaching profession, in 2014 and went on to work as a primary school teacher. However, he left the profession after less than a year to work as a caseworker for a Conservative MP and campaign for the 2015 General Election.[3]

Wragg was first elected as the MP for Hazel Grove at the 2015 general election, winning the seat from the Liberal Democrats on a swing of 15.2% and becoming the first Conservative MP there since 1997. He stood down as a councillor and, in 2016, the Liberal Democrats won the Hazel Grove ward seat back.[7]

In Parliament, Wragg currently serves on the Procedure, Education and Backbench Business Committees and previously served on the Finance Committee.[9]

In 2016 it was reported that Wragg had moved back to his parents' house in order to save money for a deposit on buying a house. This was despite earning a salary of £74,000, with his London accommodation costs covered separately by expenses.[10][11]